To find the expression for f(x) over g(x), we need to divide the function f(x) by g(x). Given:
f(x) = 6x^3 + 19x^2 + 16x^4
g(x) = x^2
We can express this as:
f(x) / g(x) = (6x^3 + 19x^2 + 16x^4) / x^2
Next, we simplify this division. We can rewrite the numerator:
- The term 6x^3 / x^2 simplifies to 6x.
- The term 19x^2 / x^2 simplifies to 19.
- The term 16x^4 / x^2 simplifies to 16x^2.
Putting this all together:
f(x) / g(x) = 6x + 19 + 16x^2
Therefore, when we combine the terms, we get:
f(x) / g(x) = 16x^2 + 6x + 19
This is the simplified form of f(x) over g(x).